* Dollar rebounds, but not far off eight-month low * Wall Street, Europe shares rise but budget, debt fears persist * U.S. one-month T-bill rates hover at highest in 10 months By Wanfeng Zhou NEW YORK, Oct 4 (Reuters) - Major stock markets edged higher on Friday but were headed for a second week of losses while the dollar hovered near an eight-month low on fears the budget standoff in Washington will drag on until politicians reach a deal to raise the U.S. debt ceiling. On Wall Street, the three major indexes were on track to end the week with steep losses, despite modest gains on Friday, as the partial U.S. government shutdown entered its fourth day and appeared likely to drag on for another week or more. While selling has been orderly so far, investors see volatility rising if the shutdown becomes prolonged, which would hurt the economic recovery. Many do not expect lawmakers to reach an agreement on the budget until they come up against the deadline to raise the U.S. government's $16.7 trillion debt ceiling to prevent a U.S. default on its debt. Treasury Secretary Jack Lew has said the government will hit the limit no later than Oct. 17. Fears of a U.S. default lifted interest rates on ultra-short-term U.S. Treasury bills to their highest levels in over 10 months on Friday, while the cost of insuring one-year U.S. government bonds against default hit the highest level since August 2011. Investor confidence was boosted Thursday afternoon when reports surfaced that House of Representatives Speaker John Boehner told his Republican party colleagues that he would not let the stalemate over the budget interfere with raising the debt ceiling. On Friday, however, Boehner said the Republican-controlled House will not vote on a "clean" spending bill without conditions to end the government shutdown and demanded spending cuts in exchange for raising the government's borrowing limit. The S&P 500 showed little movement after his brief news conference. "If there's no agreement by the end of next week, the concern will really become greater and the impact will be more pronounced," said Kate Warne, investment strategist at Edward Jones in St. Louis. Warne helps oversee $670 billion in assets. MSCI's world equity index, which tracks shares in 45 countries, edged up 0.1 percent, but was on track for a weekly loss of 0.5 percent. Top international policymakers have warned that a failure to raise the U.S. debt ceiling would be a serious blow to the world economy. On Thursday, Dennis Lockhart, president of the Federal Reserve Bank of Atlanta, said the shutdown will hurt growth in the last quarter of this year, while the Bank of Japan said an extended U.S. budget standoff would have a severe global impact. Still, many long-term investors believe Congress will eventually resolve the budget and debt issues, which would ensure that any stock pullback would be followed by a rebound. "Day by day, people are getting more tense," said Francois Savary, chief investment officer at Swiss firm Reyl. "But we are betting on the fact that a deal will be found, and this should provide us with the opportunity to increase our equity exposure." The Dow Jones industrial average gained 59.66 points, or 0.40 percent, to 15,056.14. The Standard & Poor's 500 Index rose 9.56 points, or 0.57 percent, to 1,688.22. The Nasdaq Composite Index added 31.18 points, or 0.83 percent, to 3,805.52. The S&P 500 index has fallen for nine of the past 12 sessions, but several sectors rose on Friday, including materials and healthcare stocks. European shares rose 0.1 percent to end at 1,243.74 points. The U.S. shutdown delayed the government's release of non-farm payrolls data for September, which had been scheduled for Friday. The Labor Department's monthly jobs market report has been playing a key role in the Federal Reserve's assessment of the economy in its deliberations on when to scale back its stimulus. The postponement had no noticeable market impact. The dollar rose for the first time in six days. It gained 0.5 percent to 80.136 against a basket of major currencies. The euro slipped 0.5 percent to $1.3552. The dollar hit an eight-month low on Thursday on views that the government shutdown will further delay the Fed's plans to reduce its bond-buying program. On Oct. 17, when the government is projected to reach its debt ceiling, $85 billion of Treasury bills will mature. The interest rate on that T-bill issue last traded at 0.13 percent, up 2 basis points from late on Thursday and up 9 basis points on the week. Interest rates on T-bills that mature in the first half of November last traded at 0.11 percent, 5 basis points higher than late Thursday and up 9 basis points from a week earlier. "We are seeing some real volatility in the bill sector," said Jason Rogan, managing director of Treasuries trading at Guggenheim Partners in New York. "Bills are showing the first signs of distress." The benchmark 10-year U.S. Treasury note was down 12/32, its yield at 2.646 percent. Oil prices were steady as a tropical storm approached the oil-producing regions around the Gulf of Mexico, offsetting worries that a prolonged U.S. government shutdown will dent demand. Brent crude rose 6 cents to $109.06. U.S. oil rose 13 cents to $103.44. Gold slipped to $1,308 an ounce from $1,316.69.